A279787 Twice-partitioned numbers where the first partition is constant.

1, 1, 3, 4, 10, 8, 29, 16, 64, 58, 124, 57, 469, 102, 489, 763, 1597, 298, 3858, 491, 8942, 6355, 6187, 1256, 59076, 18766, 20830, 49694, 167078, 4566, 481186, 6843, 752128, 362907, 231592, 1597802, 5951007, 21638, 790404, 2655810, 25274798, 44584, 40898731

Offset: 0

Author

Gus Wiseman, Dec 18 2016

Keywords

• nonn

Examples

			The a(4)=10 twice-partitions are:
((4)), ((31)), ((22)), ((211)), ((1111)),
((2)(2)), ((2)(11)), ((11)(2)), ((11)(11)),
((1)(1)(1)(1)).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5723
• Gus Wiseman, Illustration of the first 9 terms of A279787
• Gus Wiseman, Sequences enumerating triangles of integer partitions

Crossrefs

Cf. A000005, A000041, A018818, A063834, A260685, A271619.

Programs

Maple

with(numtheory): with(combinat):
a:= proc(n) option remember; `if`(n=0, 1,
      add(numbpart(n/d)^d, d=divisors(n)))
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 20 2016

Mathematica

nn=20;Table[DivisorSum[n,Power[PartitionsP[#],n/#]&],{n,nn}]

PARI

a(n)=if(n==0, 1, sumdiv(n, d, numbpart(n/d)^d)) \\ Andrew Howroyd, Aug 26 2018

Formula

a(n) = Sum_{d|n} A000041(n/d)^d for n > 0. - Andrew Howroyd, Aug 26 2018